\documentclass[
	solutions,
	singlenumbering,
	nopagenumber
]{../../../lib/tex/ormc_handout}
\usepackage{../../../lib/tex/macros}

\title{Warm-Up: The Painting}
\uptitler{\smallurl{}}
\subtitle{Prepared by Mark on \today.}

\begin{document}

	\maketitle

	\problem{}
	You have a painting on a string. \par
	Hang the painting on two nails so that if either is removed, the painting falls. \par

	\vspace{2mm}
	You may detach the string as you hang the painting, but it must be re-attached once you're done.

	\note{The solution to this problem isn't a \say{think outside the box} trick, it's a clever wrapping of the string.}


	\begin{center}
	\begin{tikzpicture}[scale=2.0]
		\draw[line width = 0.5mm]
			(0, 1) --
			(2, 1) --
			(2, 0) --
			(0, 0) --
			cycle
		;

		\draw[line width = 0.5mm, dotted]
			(0.1, 1) --
			(1, 1.5) --
			(1.9, 1)
		;

		\fill (1, 1.5) circle[radius = 0.25mm];


		\draw[line width = 0.2mm]
			(0.66, 0.66) --
			(0.66, 0.35) --
			(0.60, 0.1)
			(0.72, 0.1)--(0.66, 0.35)
		;

		\draw[line width = 0.2mm]
			(0.66, 0.575) --
			(0.6, 0.475) --
			(0.525, 0.575)
			(0.66, 0.575) --
			(0.72, 0.475) --
			(0.795, 0.575)
		;

		\fill[color=white] (0.66, 0.66) circle[radius = 0.8mm];
		\draw (0.66, 0.66) circle[radius = 0.8mm];
	\end{tikzpicture}
	\end{center}


	\begin{solution}

		Say we have a left nail and a right nail. The path of the string is as follows:
		\begin{itemize}
			\item Start on the left
			\item Move over both nails, wrap right nail cw
			\item Wrap left nail ccw
			\item Wrap right nail ccw
			\item Exit downwards, in between both nails
		\end{itemize}

	\end{solution}

\end{document}